Out of 267 roller skates randomly selected for close examination, 5 were found to have a loose rivet, and 12 were not cleaned according to specifications.
a. Use the formula for computing an expected count. How many roller skates would you expect to have both problems if the problems are independent?
b. Find the estimated probability of a loose rivet, using the relative frequency.
c. Similarly, find the estimated probability of a cleaning problem.
d. Use the probability formula from Chapter 6 to find the estimated probability of a loose rivet and a cleaning problem, assuming they are independent, using your estimated probabilities from parts b and c.
e. Convert your probability from part d to an expected count by multiplying it by the sample size.
f. Compare your answers to parts a (from the expected count formula) and e (from the independence formula). Comment on why they both came out this way.